Το κορίτσι τρώει παγωτό βανίλια στο πάρκο.

Not necessarily. In Greek, grammatical gender and real-life sex are not always the same thing.

κορίτσι means girl, but grammatically it is neuter, so it takes:

• το as its article
• neuter agreement with adjectives

So:

• το μικρό κορίτσι = the little girl

This feels strange to English speakers at first, but it is completely normal in Greek. You just have to learn the noun together with its grammatical gender.

τρώει is the 3rd person singular present form of τρώω = to eat.

So it means:

• he eats
• she eats
• it eats
• and, depending on context, also is eating

In this sentence, because the subject is το κορίτσι, τρώει means the girl eats / is eating.

It can mean either one, depending on context.

Greek present tense often covers both:

• a habitual meaning: eats
• an ongoing meaning: is eating

So this sentence could mean:

• The girl eats vanilla ice cream in the park
  or
• The girl is eating vanilla ice cream in the park

In normal conversation, the situation usually makes the intended meaning clear.

Greek often leaves out the indefinite article when talking about food or something non-specific.

So:

• τρώει παγωτό = she is eating ice cream
• τρώει ένα παγωτό = she is eating an ice cream / one ice cream

Adding ένα makes it sound more like one specific ice cream or an ice cream item.
Without ένα, the sentence sounds very natural and general.

In Greek, flavors are very often expressed with a noun after the food noun, almost like a label.

So:

• παγωτό βανίλια = vanilla ice cream
• παγωτό σοκολάτα = chocolate ice cream
• παγωτό φράουλα = strawberry ice cream

This is a very common everyday pattern.
You can think of βανίλια here as naming the flavor, not acting like a regular adjective.

στο is a contraction of:

σε + το → στο

That means:

• σε = in / at / to
• το = the (neuter singular)

So:

• στο πάρκο = in the park / at the park

This contraction is standard and extremely common in Greek.

It is in the case Greek expects after σε, but in this noun the form happens to look the same.

After σε, Greek uses the accusative:

• στο πάρκο

But πάρκο is a neuter noun, and in the singular, many neuter nouns have the same form in:

• nominative
• accusative

So even though the case changes grammatically, the word itself stays πάρκο.

The same thing happens with κορίτσι and παγωτό: neuter nouns often look the same in nominative and accusative singular.

Greek word order is more flexible than English.

The neutral order here is:

Το κορίτσι τρώει παγωτό βανίλια στο πάρκο.

But Greek can move parts around for emphasis or style, for example:

• Στο πάρκο το κορίτσι τρώει παγωτό βανίλια.
• Παγωτό βανίλια τρώει το κορίτσι στο πάρκο.

These alternatives can sound more marked or emphatic, but they are possible.
So yes, word order matters, but Greek is not as rigid as English.

Usually, no—not in a normal neutral sentence.

Greek uses the definite article much more often than English. So το κορίτσι is the natural way to say the girl.

If you remove the article, the sentence sounds unnatural in ordinary usage. Bare nouns do exist in Greek, but usually in special contexts such as:

• headlines
• labels
• very poetic or telegraphic styles

For everyday speech, keep το.

A simple pronunciation guide is:

to ko-RI-tsi TRO-ee pa-go-TO va-NI-lia sto PAR-ko

A few useful notes:

• κορίτσι = stress on RI
• τρώει = two syllables, roughly TRO-ee
• παγωτό = stress on the last syllable, -TO
• βανίλια = stress on NI
• πάρκο = stress on PAR

The accent marks in Greek show you which syllable gets the stress.